Prime Decomposition Theorem for Arbitrary Semigroups: General Holonomy Decomposition and Synthesis Theorem
نویسندگان
چکیده
Herein we generalize the holonomy theorem for finite semigroups (see [7]) to arbitrary semigroups, S, by embedding s^ into an infinite Zeiger wreath product, which is then expanded to an infinite iterative matrix semigroup. If S is not finite-J-above (where finite-J-above means every element has only a finite number of divisors), then S is replaced by g3, the triple Schtitzenberger product, which is finite-J-above. This paper provides global proofs inspired by previous ‘local’ proofs in the finite case. See [2,3,.5,7,8,10-131, for further background. See [8] for applications to finite semigroups. See [2,3] for further developments in the synthesis theorem.
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